We extend the classical Enriques–Petri theorem to s-subcanonical projectively normal curves, proving that such a curve is (s+2)-gonal if and only if it is contained in a surface of minimal degree. We also show that any Fermat hypersurface of degree s+2 is apolar to a s-subcanonical (s+2)-gonal projectively normal curve, and vice versa.
